Si non potes reperire Berolini in tabula, ludens essetis non WIF.
Hey, get your stinking cursor off my face! I got nukes, you know.
I think they would carry over. It doesn't make sense that you would gain influence and then lose it all because you didn't get a chance to resolve it.
Edit: also the rules seem to indicate that only diplomatic situations that were resolved are reset, not to touch anything else
Nothing in the rules says to move influence markers NOT in the "resolved this turn" box - so they stay put.